Screening-and-Selection Mechanism

• Screening-and-selection mechanism is a systematic process that first screens items with lightweight criteria and then selects a final subset with rigorous evaluation.
• It balances efficiency and accuracy by maximizing true positive rates while controlling false positives and minimizing computational costs.
• Applications span high-dimensional statistics, scientific discovery pipelines, materials science, and algorithmic hiring, with guarantees for fairness and optimality.

A screening-and-selection mechanism is a systematic procedure, algorithm, or protocol designed to filter and select a subset of items, variables, candidates, or features from a larger set based on specific criteria, often under resource or error constraints. Such mechanisms are foundational in high-dimensional statistics, scientific discovery pipelines, materials science, algorithmic hiring, and physical systems with emergent phenomena. The principal objectives typically include maximizing the retention of true positives (sensitivity), controlling false positives (specificity), optimizing efficiency or utility (e.g., minimizing shortlist size or computational cost), and, in some domains, ensuring fairness, diversity, or physical admissibility.

1. Formal Definitions and General Principles

Screening refers to an initial reduction phase in which candidates (be they individuals, features, materials, or signaling events) are evaluated with relatively lightweight, often marginal, criteria. Selection is the subsequent process whereby a final subset is chosen, usually with more stringent or resource-intensive evaluation steps. The division between screening and selection is motivated by computational, cost, or epistemic constraints: initial stages save resources by rapidly eliminating suboptimal items, while later stages invest more heavily in accurate adjudication among pre-screened candidates.

A canonical example is found in the conformal inference framework for predictive screening, which shortlists units based on calibrated $p$-value thresholds and guarantees control of the false discovery rate (FDR) (Jin et al., 2022). In high-dimensional feature selection, screening identifies a reduced subset of variables likely to be relevant, and selection applies regularized estimation or further statistical testing to select the final model (Dedecker et al., 8 Dec 2025).

2. Algorithmic Instantiations Across Domains

Screening-and-selection mechanisms are domain-adaptive and mathematically principled. Notable formalizations include:

• Conformal Screening with FDR Control: Given a training set $\{(X_i,Y_i)\}_{i=1}^n$ and test covariates $\{X_{n+j}\}_{j=1}^m$, the mechanism computes for each test unit a conformal $p$-value $p_j$ reflecting the plausibility that $Y_{n+j} > c_j$ (target threshold). Multiple testing control (Benjamini–Hochberg) is applied to $\{p_j\}$, yielding a shortlist $R$ of candidates with FDR $\leq q$ (Jin et al., 2022).
• Model-Free Marginal Screening for Variable Selection: For explanatory variables $X^{(j)}$, the screening step computes the studentized marginal regression slope $\hat\tau_j$ and its variance estimate $\hat v_j$. Variables with $|\sqrt{n}\hat\tau_j/\sqrt{\hat v_j}| \geq \gamma$ (with $\gamma$ a normal quantile for the target FPR $q$) are retained for downstream multivariate modeling (Dedecker et al., 8 Dec 2025).
• Multimodal Feature Screening with MoE Guidance: In the MoTAS framework for Alzheimer's diagnosis, input speech is augmented via TTS, feature embeddings are extracted (e.g., Wav2Vec2, MFCC, ResNet, BERT), and a Mixture-of-Experts mechanism adaptively weighs each feature modality during classification, yielding substantial gains in data-limited settings (Shao et al., 28 Aug 2025).
• Graphlet Screening in High-Dimensional Regression: The GS algorithm leverages the graph of strong dependence (GOSD) among covariates to screen only small, local connected subgraphs ("graphlets") likely to harbor signal. A penalized, multivariate "cleaning" then finalizes the selection, achieving minimax optimal Hamming error (Jin et al., 2012).
• Material Screening in Experimental Physics: The XENON100 campaign employs a seven-stage process: material identification, sample preparation, radioactivity measurement (HPGe/ICP-MS), spectral analysis, background simulation, acceptance/rejection based on strict background contribution thresholds, and integration. Acceptance demands empirical activities below calculated limits to maintain aggregate backgrounds below $10^{-2}$ events/keV/kg/day (Collaboration et al., 2011).

3. Theoretical Guarantees and Optimality

Screening-and-selection mechanisms often come equipped with rigorous, finite-sample, or asymptotic guarantees:

• Sure Screening Property (SSP) and FPR Control: For model-free variable screening, with high probability, all signal variables are included (SSP), and the empirical FPR converges to the target rate $q$: $$\mathbb{P}(\mathcal{M}^* \subseteq \widehat{\mathcal{M}}) \to 1, \quad |\mathbb{E}[\widehat{\mathcal{M}} \cap \mathcal{M}^c]/|\mathcal{M}^c| - q| \to 0$$ as $n \to \infty$, under finite high-order moment conditions (Dedecker et al., 8 Dec 2025).
• Finite-Sample FDR Control: In conformal prediction-based screening,

$$\mathrm{FDR} = \mathbb{E} \left[ \frac{\sum_{j \in R} 1\{ Y_{n+j} \leq c_j \} }{|R| \vee 1} \right] \leq q$$

under (exchangeability, monotonicity), independently of the predictive model used (Jin et al., 2022).

• Minimax Optimality in High Dimensions: The GS procedure attains the minimax Hamming loss rate in rare-weak signal regimes, outperforming the lasso and subset-selection in nontrivial parameter domains (Jin et al., 2012).
• Anytime Valid Selection: Sequential Correct Screening (SCS) yields a family of subsets $\hat S_T$ such that, at all times $T$, $\mathbb{P}(S \subseteq \hat S_T) \geq 1 - \alpha$, and ultimately $\hat S_T$ converges exactly to the true top-$m$ set (Toyoda et al., 20 Aug 2025).

4. Fairness, Diversity, and Strategic Manipulation

Beyond classical utility or error rates, screening-and-selection mechanisms are increasingly adapted to meet additional constraints:

• Fairness via Sequential Pipeline Adjustment: In multi-stage pipelines with group-specific pass rates, one may impose Equality of Opportunity (EO) by tuning promotion probabilities $\pi^j_{X1}$ so that all groups have equal true-positive passage rates. The optimal policy under EO, the "Opportunity-Ratio Policy," is provably unique for maximizing precision. Additional constraints, such as group-blindness or Equalized Odds, can be incorporated but always reduce achievable efficiency (Blum et al., 2022).
• Calibrated Subset Selection (CSS): CSS constructs explicit, distribution-free shortlisting thresholds for classifiers, guaranteeing that the expected number of qualified candidates in a shortlist meets or exceeds a target $k$ with probability $1-\alpha$. Group-calibrated variants ensure per-group diversity guarantees regardless of classifier calibration or pool distribution (Wang et al., 2022).
• Strategic Sequential Pipelines: Sequential ordering of screening criteria permits "zig-zag" exploitation by strategic subjects, who minimize their manipulation cost by alternating which classifiers to satisfy at each stage. A conservative, provably optimal defense is to $\tau$-shift the thresholds of each test, ensuring zero false positives even under adversarial manipulation (Cohen et al., 2023).

5. Computational Complexity and Practical Considerations

Efficiency is a primary motivation for most screening-and-selection designs:

• Marginal Screening: Model-free variable screening operates in $O(np)$ time, scalable to $p \gg n$ (Dedecker et al., 8 Dec 2025).
• Graphlet Screening: By restricting testing to small connected subgraphs (size $\le m_0$ with typical max degree $K$), the screening cost is $O(p (\log p)^k)$, a dramatic reduction from brute-force multivariate subset screening (Jin et al., 2012).
• Randomized Aggregation Methods: GDS-ARM avoids the combinatorial blowup of fitting all main-effect and interaction models by randomly sampling submodels and aggregating selection results, maintaining high power and low error (Singh et al., 2022).
• Multimodal Data Pipelines: In MoTAS, mixture-of-experts gating selects informative modalities and suppresses noise, yielding robustness in training regimes with limited data (Shao et al., 28 Aug 2025).
• Instance/Feature Screening in Deep Forests: Hashing mechanisms prune redundant feature groups with $O(Rmc)$ cost, and self-adaptive instance screening accelerates early stopping, reducing training time by 30–45% on high-dimensional tasks (Ma et al., 2022).

6. Screening-and-Selection in Physical and Emergent Systems

Screening-and-selection is not limited to information-processing disciplines:

• Parameter Selection in Amorphous Solids: Strained amorphous media develop screening lengths $\ell_e=1/\kappa_e$ and $\ell_o=1/\kappa_o$, which are not microscopic constants but emergent, protocol-dependent parameters fixed by boundary-value secular equations. The system "selects" $(\kappa_e, \kappa_o)$ according to maximization of the screened response amplitude, subject to boundary constraints (Kaur et al., 17 Sep 2024).
• Multi-Field Screening in Modified Gravity: In scalar-tensor theories, multi-field "Axio-Chameleon" mechanisms screen long-range forces via the interplay of axion and dilaton gradients. Screening is protocol-specific and depends on the geometry and scale of the source, offering suppression factors analogous to single-field chameleon mechanisms but with technical naturalness and string-theoretic compatibility (Brax et al., 2023).

7. Summary Table: Representative Screening-and-Selection Mechanisms

Domain	Mechanism/Algorithm	Guarantee/Objective
Feature selection	Model-free screening (Dedecker et al., 8 Dec 2025)	SSP, FPR control, $\mathcal{O}(np)$
Scientific pipelines	Conformal+B-H (Jin et al., 2022)	Finite-sample FDR guarantee
Hiring, admissions	EO-adjusted promotion (Blum et al., 2022)	Fairness with optimal precision
High-dim regression	Graphlet Screening (Jin et al., 2012)	Minimax error, reduced computation
Materials science	XENON100 workflow (Collaboration et al., 2011)	Per-component radioactivity limits
Screening with diversity	Calibrated CSS (Wang et al., 2022)	Distribution-free quota guarantees

Each mechanism implements the general principle of efficiently reducing a large candidate space to a vetted subset that meets rigorous statistical, physical, or operational constraints, often adapting dynamically to data geometry, adversarial behavior, or group composition. Theoretical guarantees depend on the underlying assumptions (exchangeability, moment conditions, group structure, etc.), and algorithms must be tuned to the application-specific balance of power, FDR/FPR, fairness, and computational tractability.